On Ramsey (3K_2,2K_5)-Minimal Graphs
Abstract
For given two graphs G and H, the notation F?(G,H) means that any red-blue coloring of all the edges of F contains a red copy of G as a subgraph or a blue copy of H as a subgraph. A graph F is Ramsey (G,H)-minimal if F?(G,H) and for any edge e in F then F-e?(G,H). The class of all (G,H)-minimal graph, is denoted by R(G,H). In this research, we determined graphs in R(3K2,2K5Â ).
References
Baskoro, E. T., and Wijaya, K. (2015). On Ramsey (2K_2,C_4)-Minimal Graphs. Springer Proceedings in Mathematics & Statistics, 98, pp 11-17.
Baskoro, E. T., & Yulianti, L. (2011). On Ramsey minimal graphs for 2K_2 versus P_n. Advanced and Applications in Discrete Mathematics, 8(2), 83–90.
Burr, S. A., Erdos, P., Lovasz, L. (1976). On Graph of Ramsey Type. Ars Combinatoria, 167–190.
Burr, S. A., E. (1978). A class of Ramsey-finite graphs, Congr. Numer. Congr. Numer, 21, 171–180.
Hadiputra, F. F., & Silaban, D. R. (2021). Infinite Family of Ramsey ?(K?_1,2,C_4)-minimal Graphs. Journal of Physics:
Conference Series, 1722(1). https://doi.org/10.1088/1742-6596/1722/1/012049
Ramsey, F. P. (2009). On a Problem of Formal Logic. Classic Papers in Combinatorics, 1–24. https://doi.org/10.1007/978-0-8176-4842-8_1
Silaban, D. R., Taufiq, A. I., Wijaya, K. (2008). On Ramsey (mK_2,P_4)-Minimal Graphs. SIAM Journal on Discrete Mathematics, 22(2), 467–488. https://doi.org/10.1137/050647116
Tatanto, D., & Baskoro, E. T. (2012). On Ramsey (2K_2,2P_n)-minimal graphs. AIP Conference Proceedings, 1450, 90–95. https://doi.org/10.1063/1.4724122
Wijaya, K., Baskoro, E. T., Assiyatun, H., Suprijanto, D. (2015). The Complete List of (2K_2,K_4)-Minimal Graphs. Electronic Journal of Graph Theory and Applications, 3, 216–227.
Wijaya, K., Yulianti, L., Baskoro, E. T., Assiyatun, H., Suprijanto, D. (2015). All Ramsey (2K_2,C_4)-Minimal Graphs. J. Algorithms Comput., 46, 9–25. https://d1wqtxts1xzle7.cloudfront.net/84297624/article_7922_651e3bc41b32f240cb33e7a9669c32df-libre.pdf?1650166454=&response-content-disposition=inline%3B+filename%3DAll_Ramsey_2_K_2_C_4_Minimal_Graphs.pdf&Expires=1670263574&Signature=Ud26erEc3rI~MidtzGsYz
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2015). On Unicyclic Ramsey (mK_2,P_3)-Minimal Graphs. Procedia Computer Science, 74, 10–14. https://doi.org/10.1016/j.procs.2015.12.067
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2016). On Ramsey (3K_2,K_3)- Minimal graphs. AIP Conference Proceedings, 1707, 9–25. https://doi.org/10.1063/1.4940826
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2018). On Ramsey (4K_2,P_3)-minimal graphs. AKCE International Journal of Graphs and Combinatorics, 15(2), 174–186. https://doi.org/10.1016/j.akcej.2017.08.003
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2020). Subdivision of graphs in R(mK_2,P_4). Heliyon, 6(6), e03843. https://doi.org/10.1016/j.heliyon.2020.e03843
Wijaya, K., Baskoro, E. T., Taufik, A. I., & Silaban, D. R. (2022). On Ramsey Minimal Graphs for a 3-Matching Versus a Path on Five Vertices. Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021), 96, 8–11. https://doi.org/10.2991/acsr.k.220202.001
Baskoro, E. T., & Yulianti, L. (2011). On Ramsey minimal graphs for 2K_2 versus P_n. Advanced and Applications in Discrete Mathematics, 8(2), 83–90.
Burr, S. A., Erdos, P., Lovasz, L. (1976). On Graph of Ramsey Type. Ars Combinatoria, 167–190.
Burr, S. A., E. (1978). A class of Ramsey-finite graphs, Congr. Numer. Congr. Numer, 21, 171–180.
Hadiputra, F. F., & Silaban, D. R. (2021). Infinite Family of Ramsey ?(K?_1,2,C_4)-minimal Graphs. Journal of Physics:
Conference Series, 1722(1). https://doi.org/10.1088/1742-6596/1722/1/012049
Ramsey, F. P. (2009). On a Problem of Formal Logic. Classic Papers in Combinatorics, 1–24. https://doi.org/10.1007/978-0-8176-4842-8_1
Silaban, D. R., Taufiq, A. I., Wijaya, K. (2008). On Ramsey (mK_2,P_4)-Minimal Graphs. SIAM Journal on Discrete Mathematics, 22(2), 467–488. https://doi.org/10.1137/050647116
Tatanto, D., & Baskoro, E. T. (2012). On Ramsey (2K_2,2P_n)-minimal graphs. AIP Conference Proceedings, 1450, 90–95. https://doi.org/10.1063/1.4724122
Wijaya, K., Baskoro, E. T., Assiyatun, H., Suprijanto, D. (2015). The Complete List of (2K_2,K_4)-Minimal Graphs. Electronic Journal of Graph Theory and Applications, 3, 216–227.
Wijaya, K., Yulianti, L., Baskoro, E. T., Assiyatun, H., Suprijanto, D. (2015). All Ramsey (2K_2,C_4)-Minimal Graphs. J. Algorithms Comput., 46, 9–25. https://d1wqtxts1xzle7.cloudfront.net/84297624/article_7922_651e3bc41b32f240cb33e7a9669c32df-libre.pdf?1650166454=&response-content-disposition=inline%3B+filename%3DAll_Ramsey_2_K_2_C_4_Minimal_Graphs.pdf&Expires=1670263574&Signature=Ud26erEc3rI~MidtzGsYz
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2015). On Unicyclic Ramsey (mK_2,P_3)-Minimal Graphs. Procedia Computer Science, 74, 10–14. https://doi.org/10.1016/j.procs.2015.12.067
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2016). On Ramsey (3K_2,K_3)- Minimal graphs. AIP Conference Proceedings, 1707, 9–25. https://doi.org/10.1063/1.4940826
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2018). On Ramsey (4K_2,P_3)-minimal graphs. AKCE International Journal of Graphs and Combinatorics, 15(2), 174–186. https://doi.org/10.1016/j.akcej.2017.08.003
Wijaya, K., Baskoro, E. T., Assiyatun, H., & Suprijanto, D. (2020). Subdivision of graphs in R(mK_2,P_4). Heliyon, 6(6), e03843. https://doi.org/10.1016/j.heliyon.2020.e03843
Wijaya, K., Baskoro, E. T., Taufik, A. I., & Silaban, D. R. (2022). On Ramsey Minimal Graphs for a 3-Matching Versus a Path on Five Vertices. Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021), 96, 8–11. https://doi.org/10.2991/acsr.k.220202.001
Published
2024-07-30
How to Cite
PERMATAPUTRI, Nailul Yuni.
On Ramsey (3K_2,2K_5)-Minimal Graphs.
Jurnal Edumatika, [S.l.], v. 1, n. 1, p. 11-15, july 2024.
ISSN 0000-0000.
Available at: <https://ojs.unitas-pdg.ac.id/index.php/edumatika/article/view/1040>. Date accessed: 18 jan. 2025.
Section
Articles
